integral of ((5-10x^2)/(4x^3-6x+15))

解答

\int (\frac{5 - 10 x ^{2}}{4 x ^{3} - 6 x + 15}) d x

- \frac{5}{6} ln 4 x^{3} - 6 x + 15 + C

求解步骤

\int \frac{5 - 10 x ^{2}}{4 x ^{3} - 6 x + 15} d x

使用换元积分法

= \int - \frac{5}{6 u} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{5}{6} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{5}{6} ln ∣ u ∣

u = 4 x^{3} - 6 x + 15

代回

= - \frac{5}{6} ln 4 x^{3} - 6 x + 15

解答补常数

= - \frac{5}{6} ln 4 x^{3} - 6 x + 15 + C

d er i v a t i v e f (x) = x x^{2} + 21

x \to \infty lim (1 + 4 x)

x^{2} \frac{d y}{d x} - x y + 1 = 0

x \to \infty lim (- \frac{x}{x})

\int_{0}^{3} 2 e^{x} d x